不同网格扭曲率下压力修正全隐算法——IDEAL求解性能研究

2008年,本文作者和陶文铨等提出了一种用于速度和压力耦合求解的高效稳定压力修正全隐算法IDEAL,该算法通过在每个迭代层次上对压力方程进行两次内迭代计算,完全克服了SIMPLE算法的两个假设,充分满足了速度和压力之间的耦合,从而大大提高了计算的收敛性和健壮性。为了进一步实现IDEAL算法的推广应用,本文基于三维倾斜方腔顶盖驱动流动,研究了IDEAL算法在不同网格扭曲率下的求解特性。研究发现,在不同网格扭曲率下,IDEAL算法的健壮性和收敛性均优于SIMPLE算法,特别在高网格扭曲率情况下,IDEAL算法求解性能更加优于SIMPLE算法。在不同网格扭曲率下,IDEAL算法健壮性保持不变,几乎可以在任意速度亚松弛因子下获得收敛的解,同时IDEAL算法最短计算耗时较SIMPLE算法减少了56%~89%,验证了IDEAL算法的优越性。     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散；扩散项的离散采用二阶中心差分格式；对于压力-速度耦合利用SIMPLE算法进行处理；计算节点的布置采用同位网格技术，界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算，讨论了非结构化同位网格有限体积法在实现SIMPLE算法时，迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知，本文的方法是准确和可信的。     

用任意不规则网格求解N-S方程

引入辅助点法开发了新的通量近似计算方法，建立了采用任意不规则畸变网格作为控制体积的单元中心有限体积求解Navier—Stokes的方法。它以同位网格作为变量布置方式，压力一速度耦合采用SIMPLE方法。数值算例表明，该算法对高度不规则的畸变网格适应性强；其改进了传统算法在不规则网格下计算的困难，保证了模型在高扭曲度的网格下的整体计算精度不受网格拉伸畸变和剪切畸变的影响。     

不可压缩N-S方程的稳定分步算法及耦合离散

在有限增量微积分(finite increment calculus, FIC)的理论框架下，通过引入一个附加变量，发展了压力稳定型分步算法，有效改善了经典 分步算法的压力稳定性，同时还避免了标准FIC方法中存在的空间高阶导数的计算. 为保证 数值方法同时具有较快的计算速度和较好的健壮性，发展了有限元与无网格的耦合空间离散 方法. 该方案可在网格发生扭曲的区域采用无网格法空间离散以保证求解的精度和稳定性， 而在网格质量较好的区域以及本质边界上保留使用有限元法空间离散以提高计算效率和便于 施加本质边界条件. 方腔流考题的数值模拟结果突出地显示了所发展的压力稳定型分步算 法比经典分步算法具有更好的压力稳定性，能够有效消除速度-压力插值空间违反LBB条件而 导致的压力场的虚假数值振荡. 平面Poisseuille流动和一个典型型腔充填过程的数值模拟 结果, 表明了发展的耦合离散方案相对于单一的有限元法和单一的无网格法在综合考虑计 算效率和算法健壮性方面的突出优点.     

基于贴体网格的VOF方法数模流场研究

提出了一种基于VOF方法的模拟具有复杂边界形状结构物附近流场的新算法,BFC—SIMPLE—VOF算法。采用坐标变换方法实现了任意复杂区域的结构化网格划分,在贴体网格下对二维不可压缩粘性流体的控制方程进行了离散。提出了基于交错网格的修正SIMPLE算法来迭代求解压力一速度场,修正了贴体坐标下的界面跟踪方法（VOF方法）...     

基于同位网格下求解N-S方程的快速算法

在有限容积法基础上建立了基于同位网格的SIMPLEM算法。此算法使初始压力场与速度场耦合,让压力场和速度场同时更好地满足动量方程和连续性方程,且兼顾考虑扩散对流项对计算节点速度修正值的影响及源项与速度场之间的同步性,详细给出了算法的推导过程且对方腔顶盖驱动流进行了数值模拟。计算节点的布置采用同位网格技术,界面流速通过动量插值确定,在不同条件下讨论了迭代次数与残差的关系和不同算法的收敛性,同时验证了算法及程序是准确和可信的。     

同位网格上SIMPLE算法收敛特性的Fourier分析

应用Fourier方法研究了同位网格上SIMPLE算法求解浅水方程的收敛特性,并就松弛因子组合及阻力项的影响进行了分析.结果表明,采用合适的松弛因子组合可以很快地消除高频区域的误差,同时也可逐步消减迭代中低频区域的误差以获得收敛解.在保证收敛的前提下,低频误差分量决定了迭代速度,而且浅水方程中阻力项越大越利于SIMPLE算法收敛.     

流固耦合分析的一种改进CBS有限元算法

针对流固耦合问题, 发展了一种基于任意拉格朗日-欧拉(ALE)描述有限元法的弱耦合分区算法. 运用半隐式特征线分裂算法求解Navier-Stokes方程, 在压力Poisson 方程中引入质量源项以满足几何守恒律; 运用子块移动技术更新动态网格, 并配以光滑处理防止网格质量下降; 采用Newmark-β 法求解结构运动方程. 为保持流体-结构界面处速度和动量守恒, 利用修正结合界面边界条件方法求解界面处速度通量和动量通量. 运用本方法分别模拟了不同雷诺数下单圆柱横向和两向流致振动、串列双圆柱两向流致振动. 计算表明, 本文方法计算效率高, 计算结果与已有实验和数值计算数据吻合.     

模型燃烧室内瞬态紊流的大涡模拟

本文采用三种不同亚网格尺度模型对带有V型稳定器的模型燃烧室二维瞬态紊流流动进行了大涡模拟。并在交错网格系下用SIMPLE算法和混合差分格式求解离散方程。数值研究拟不同型式入口速度分布和不同亚网格尺度模型下模型燃烧室二维瞬态紊流流场。计算结果表明不同入口速度分布和不同亚网格尺度模型对瞬态流场和出口速度分布有一定的影响。本文通过数值模拟,揭示了V型稳定器后旋涡的产生和脱落过程。通过计算结果及实验数据的比较可知,本文采用的亚网格尺度模型可以用来模拟模型燃烧室紊流流场及稳定器后面回流区的流动情况。     

非光滑方程组方法在求解非匹配网格接触问题中的应用

将非光滑方程组方法与Mortar StS接触模型(Mortar Segment-to-Segment)相结合,来求解接触面网格非匹配时的弹性接触问题.其中,非光滑方程组方法是求解弹性摩擦接触问题的有效方法,具有精确满足接触条件、迭代算法收敛性有理论保证的优点,但目前仅用于求解网格匹配的接触问题.Mortar StS接触模型可以较为方便地处理网格非匹配接触问题,其特点是不引入过多约束,满足接触分片检验条件,但目前大都采用“试验-误差”迭代方法求解控制方程,对于复杂接触问题,其收敛性不易保证.因此,将二者结合来处理网格非匹配接触问题,既可以提高求解精度,又能使得算法的收敛性得到理论保证.数值算例对接触分片检验和算法的计算精度进行了验证.     

Performance analysis of IDEAL algorithm for three‐dimensional incompressible fluid flow and heat transfer problems

Recently, an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called inner doubly iterative efficient algorithm for linked equations (IDEAL), has been proposed by the present authors. In the algorithm there exist inner doubly iterative processes for pressure equation at each iteration level, which almost completely overcome two approximations in SIMPLE algorithm. Thus, the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of solution process. However, validations have only been conducted for two‐dimensional cases. In the present paper the performance of the IDEAL algorithm for three‐dimensional incompressible fluid flow and heat transfer problems is analyzed and a systemic comparison is made between the algorithm and three other most widely used algorithms (SIMPLER, SIMPLEC and PISO). By the comparison of five application examples, it is found that the IDEAL algorithm is the most robust and the most efficient one among the four algorithms compared. For the five three‐dimensional cases studied, when each algorithm works at its own optimal under‐relaxation factor, the IDEAL algorithm can reduce the computation time by 12.9–52.7% over SIMPLER algorithm, by 45.3–73.4% over SIMPLEC algorithm and by 10.7–53.1% over PISO algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

基于涡粘性模型的翼型湍流流场熵产率计算

利用有限体积法实现了基于非正交同位网格的SIMPLE算法。基于熵分析方法,采用涡粘性模型求解湍流熵产方程,系统研究了湍流模型对二维翼型绕流流场熵产率的影响。通过计算NACA0012翼型在来流雷诺数为2.88×10⁶时,0°攻角~16.5°攻角范围内的翼型表面压力系数分布和升阻力特性,验证了算法及程序的正确性。结果表明,选择不同湍流模型时,翼型流场熵产的计算结果存在差异,湍流耗散是引起流场熵产的主要原因;翼型流场的熵产主要发生在翼型前缘区、壁面边界层和翼型尾流区域,流场熵产率与翼型阻力系数线性相关;当产生分离涡时,粘性耗散引起的熵产下降。     

Implementation of CLEAR algorithm on non‐orthogonal curvilinear co‐ordinates for solution of incompressible flow and heat transfer

In this paper, the CLEAR (coupled and linked equations algorithm revised) algorithm is extended to non‐orthogonal curvilinear collocated grids. The CLEAR algorithm does not introduce pressure correction in order to obtain an incompressible flow field which satisfies the mass conservation law. Rather, it improves the intermediate velocity by solving an improved pressure equation to make the algorithm fully implicit since there is no term omitted in the derivation process. In the extension of CLEAR algorithm from a staggered grid system in Cartesian coordinates to collocated grids in non‐orthogonal curvilinear coordinates, three important issues are appropriately treated so that the extended CLEAR can lead to a unique solution without oscillation of pressure field and with high robustness. These three issues are (1) solution independency on the under‐relaxation factor; (2) strong coupling between velocity and pressure; and (3) treatment of the cross pressure gradient terms. The flow and heat transfer problems in a rectangular enclosure with an internal eccentric circle and the flow in a lid‐driven inclined cavity are computed by using the extended CLEAR. The results show that the extended CLEAR can guarantee the solution independency on the under‐relaxation factor, the smoothness of pressure profile even at very small under‐relaxation factor and good robustness which leads to a converged solution for the small inclined angle of 5^° only with 5‐point computational molecule while the extended SIMPLE‐series algorithm usually can get a converged solution for the inclined angle larger than 30^° under the same condition. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical simulation of forced convection of nanofluid in a confined jet

In this paper two-dimensional incompressible water–Al₂O₃ nanofluid flow in a confined jet in the laminar flow regime is numerically investigated. A finite volume technique on a collocated grid is employed for discretizing the governing equations by applying the SIMPLE algorithm to link the pressure and velocity fields. The present computations are in a very good agreement with experimental results in open literature.     

A new method for accelerating the rate of convergence of the simple-like algorithm

A pressure correction formula is proposed for the SIMPLE-like algorithm in order to improve the rate of the convergence when solving laminar Navier–Stokes equations when there is rapidly varying pressure. Based on global mass conservation, a line average pressure correction is derived by integration of the momentum equation for approximate one-dimensional flow. The use of this formula with the SIMPLE-like algorithm can rapidly build up the pressure distribution in the region where the pressure undergoes a very large change, which normally causes the rate of convergence of the SIMPLE or the SIMPLEC schemes to be slow. In order to illustrate the technique, the performances of SIMPLE and of SIMPLEC with the average pressur correction are investigated for axisymmetric flow past and through a sampler. A comparison of these two techniques shows that the average pressure correction proposed in this paper significantly accelerates the rate of convergence.     

Comparison of several open boundary numerical treatments for laminar recirculating flows

Several open boundary conditions (OBCs) are compared and evaluated in the framework of the SIMPLE algorithm using staggered and non-staggered grid systems. The benchmark laminar flow test cases used for the OBC evaluation are Poiseuille-Benard flow in a channel and stratified backward-facing step flow. The investigated OBCs are linear explicit step space extrapolation, Orlanski's monochromatic wave, and pressure extrapolation. Orlanski's and pressure extrapolation open boundary treatment for unsteady and steady flows, respectively, yield little reflection and has proved to be adequate for engineering calculations.     

Development of new finite volume schemes on unstructured triangular grid for simulating the gas–liquid two‐phase flow

This paper presents a coupled finite volume inner doubly iterative efficient algorithm for linked equations (IDEAL) with level set method to simulate the incompressible gas–liquid two‐phase flows with moving interfaces on unstructured triangular grid. The finite volume IDEAL method on a collocated grid is employed to solve the incompressible two‐phase Navier–Stokes equations, and the level set method is used to capture the moving interfaces. For the sake of mass conservation, an effective second‐order accurate finite volume scheme is developed to solve the level set equation on triangular grid, which can be implemented much easier than the classical high‐order level set solvers. In this scheme, the value of level set function on the boundary of control volume is approximated using a linear combination of a high‐order Larangian interpolation and a second‐order upwind interpolation. By the rotating slotted disk and stretching and shrinking of a circular fluid element benchmark cases, the mass conservation and accuracy of the new scheme is verified. Then the coupled method is applied to two‐phase flows, including a 2D bubble rising problem and a 2D dam breaking problem. The computational results agree well with those reported in literatures and experimental data. Copyright © 2015 John Wiley & Sons, Ltd.     

A robust algorithm for computing fluid flows on highly non‐smooth staggered grids

A new method for computing the fluid flow in complex geometries using highly non‐smooth and non‐orthogonal staggered grid is presented. In a context of the SIMPLE algorithm, pressure and physical tangential velocity components are used as dependent variables in momentum equations. To reduce the sensitivity of the curvature terms in response to coordinate line orientation change, these terms are exclusively computed using Cartesian velocity components in momentum equations. The method is then used to solve some fairly complicated 2‐D and 3‐D flow field using highly non‐smooth grids. The accuracy of results on rough grids (with sharp grid line orientation change and non‐uniformity) was found to be high and the agreement with previous experimental and numerical results was quite good. Copyright © 2008 John Wiley & Sons, Ltd.